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WS-07, Dielectric Substrate Characterization
Complex Permittivity Measurements with Complex Permittivity Measurements with SplitSplit--Post ResonatorPost Resonator
Jerzy Krupka
Warsaw University of Technology, Koszykowa 75, 00-662 Warsaw, Poland
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WS-07Outline of Presentation
• Dielectric resonators in complex permittivity measurements
• Theory of split post dielectric resonators
• Measurement uncertainties and resolution
• Results of measurements
• Split post for ferrite substrates characterization
• Conclusions
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Dielectric resonators use in complex permittivity measurements of substrates (history)
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[1] J. DelaBalle, P. Guillon and Y. Garault, AEUElectronics and Communication, vol. 35, pp.80-83, 1981.[2] J. Krupka and Sz. Maj, CPEM '86 Conference, pp.154-155, Gaithersburg, Maryland, 23-27 June 1986.[3] T. Nishikawa, K. Wakino, H. Tanaka, and Y. Ishikawa, CPEM ’88 Conference, pp. 154-155, 1988[4] J. Krupka, R.G. Geyer, J. Baker-Jarvis, and J. Ceremuga, DMMA'96 Conference, Bath, pp.21-24, U.K. 23-26 Sept. 1996.
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WS-07Schematic diagram of a split post dielectric resonator
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Photographs of split post dielectric resonators
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WS-07Electromagnetic filed distribution in 1.44 GHz SPDR
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Electric field in empty resonator WS-07
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Electric field in a presence of a sample having h=0.2 mm and permittivity 300
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WS-07Complex permittivity determination
h),(εKhfff
1ε 'rε0
s0'r
−+=
h - the thickness of the sample under test
f0 - the resonant frequency of the empty SPDR
fs - the resonant frequency of the SPDR with the dielectric sample
Kε - a function of and h (computed and tabulated for specific SPDR)
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WS-07Complex permittivity determination
es1
c1
DR1 )/pQQ (Qtan −−− −−=δ
h),ε(Kεhdv(v)ε
dvε
WW
p 'r1
'r
S
et
eses =
⋅
⋅
==
∫∫∫
∫∫∫
V
VS
*
*
EE
EE
h),(εKQdsR
dvµQ '
r2c0
S
*ττS
V
*0
c =⋅
⋅=
∫∫
∫∫∫HH
HH
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WS-07Uncertainties
ε
ε
εε
KK
hhT
r
r ∆+
∆=
∆'
'
1 < T < 2
hg∆hgT
L∆LT
D∆DT
εd∆εdT
hr∆hrT
dr∆drT
K∆K
hgLD
εdhrdrε
ε
+++
+++=
0.5%hg∆hg 0.2%,
L∆L 0.1%,
D∆D
0.2%,εd∆εd 0.5%,
hr∆hr 0.1%,
dr∆dr
===
===
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Ucertainties WS-07
h∆hT0.15%
ε∆ε
'r
'r +≤ 1 < T < 2
0
10
20
30
40
50
0.00001 0.0001 0.001 0.01
h=hg
εr=4.44
εr=2.36
εr=10.0
tanδ
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Limits for permittivity measurements
400
600
800
1000
1200
1400
1600
1 10 100 1000 10000
f (MHz)
εr
hs=0.1 mm
hs=0.2 mm
hs=0.4 mm
hs=0.8 mm
hs=1.5 mm
hs=2.8 mm
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WS-07Thin dielectric films measurements
1)1(
−
−<<
∆
s
f
s
s hhh
εε
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Permittivity versus frequency shift for thin films deposited on MgO substrate having 10 mm diameter and 0.5 mm thickness for 10 GHz split post
200
400
600
800
1000
0 20 40 60 80 100 120 140
εr
f-fs(MHz)
1500 nm500 nm 1000 nm
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Loss tangent resolution for thin films deposited on a MgO substrate having 10 mm diameter and 0.5 mm thickness for 10 GHz split post
10-5
10-4
10-3
200 400 600 800 1000
∆tanδ
εr
1500 nm
1000 nm
500 nm
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Results of measurements on standard reference materials
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SPDR data Reference data
f(GHz) 'rε tanδ '
rrε tanδ Material
3.9 9.420 2.40E-05 9.400 1.0E-05 Sapphire 1.4 4.448 1.15E-05 4.443 1.5E-05 Quartz 2.0 4.454 1.82E-05 4.443 1.5E-05 Quartz 3.9 4.443 2.58E-05 4.443 1.5E-05 Quartz 5.5 4.439 3.40E-05 4.443 1.5E-05 Quartz
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Measurements of stacked polymer films
Number of films
h (mm) εr tanδ (10−4)
1 0.100 3.19 49 2 0.201 3.20 50 3 0.303 3.20 50 4 0.406 3.20 49 5 0.511 3.19 49 6 0.616 3.18 50
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WS-07Split post for ferrite substratescharacterization
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WS-07Radial and axial components of themagnetic field in split post dielectric resonator
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WS-07Single dielectric post for ferrite substrates characterization
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Permittivity of YIG measured in split post resonator
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J.Krupka et al., Measurement Science and Technology, vol. 10, pp.1004–1008, November 1999
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Permeability of YIG substrates measured in split post resonator
0.400
0.500
0.600
0.700
0.800
0.900
1.000
5.5 6 6.5 7 7.5 8 8.5
0.383 mm0.508 mm0.383 mm0.508 mm
µ
f(GHz)
µ⊥
µ||
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Magnetic losses of YIG substrates measured in split post resonator
0.000
0.001
0.002
0.003
0.004
0.005
0.006
0.007
5.5 6 6.5 7 7.5 8 8.5
0.383 mm0.508 mm0.383 mm0.508 mm
tan(µ)
f(GHz)
tan(µ||)
tan(µ⊥)
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WS-07Cryogenic split post resonator
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Sketch of a split post dielectric resonator used for adhesive cure monitoring
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Conclusions
Split post dielectric resonators are one of the most convenient tools for permittivity and dielectric loss tangent determination of laminar type dielectric materials at frequencies from 1 GHz to 20 GHz
Single post and split post dielectric resonators can be used for measurements of the complex permittivity and complex permeability of ferrite substrates
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